14.6.1. Mass Distribution

Try these first

1. 1.

   What happens to the natural frequency if we add mass to a structure?

   Hint

   Think about the relationship described in the section.

2. 2.

   Define resonance in your own words.

   Hint

   It relates to the vibrations experienced by structures.

3. 3.

   What effect does adding mass to a structure have on its natural frequency?

   • Increases frequency
   • Decreases frequency
   • No effect

   Hint

   Remember the formula for natural frequency.

4. 4.

   True or False: Uneven mass distribution can lead to regular modal responses.

   • True
   • False

   Hint

   Think about how mass is arranged in a structure.

5. 5.

   A newly designed building has a mass that is unevenly distributed. Describe how this affects its performance during an earthquake.

   Hint

   Consider the effects of uneven distribution.

6. 6.

   Calculate the change in natural frequency for a structure if its mass increases from 2000 kg to 2400 kg, assuming the stiffness remains constant and initially the natural frequency is 2 Hz.

   Hint

   Use the formula for natural frequency: f = 1/(2π)√(k/m).